How to make Shadows-Only Render
While Shady Puck's answer covers making a true shadow-only render, here is my approach to creating this type of render using the Cycles Toon shader in combination with a shadow pass and some manual contrast adjustment.

My final result:


Thanks to MrChimp2313 for the awesome CC-0 house model!



First just give everything a white Toon shader material, this will help with that contrasty, cartoony look.  The Toon shader also has two other properties (besides color), you should set the Size to something fairly high (close to 1.0) and leave the Smooth at 0.0.

Light the scene with a single sun lamp, with a fairly small shadow size.  Tweak the direction and strength to suit your tastes for your scene.

Set the environment color to Black, this way the shadows and highlights will all come from the sun lamp.

Make sure to turn on the Shadow render pass and render your image.  Keep in mind that for this effect to work you need to eliminate as much noise as possible, so use a lot of samples.

In the compositor, run the shadow pass image itself through a Color Ramp node.  You can tweak the swatches' positions to get the effect you are looking for, but the basic idea is to have them fairly close together to get that super high-contrast shadowy look.  I also found it looks a little more pleasing if you adjust the minimum color to be not pure black.